Final answer:
The solution set for the equation 3(5s-4)+15=4(s-3)-(-10s+1) is s = -16, found by expanding, simplifying, and solving for s.
Step-by-step explanation:
To solve the equation 3(5s-4)+15=4(s-3)-(-10s+1), we need to expand and simplify both sides, and then collect like terms to isolate the variable s. Here are the steps:
- Distribute the 3 into the first set of parentheses on the left side: 3*5s - 3*4 + 15.
- Expand the right side by distributing the 4 into the parentheses and changing the sign in front of the last set of parentheses: 4*s - 4*3 +10s - 1.
- Simplify both sides: 15s - 12 + 15 = 4s - 12 + 10s - 1.
- Combine like terms: 15s + 3 = 14s - 13.
- Subtract 14s from both sides to get s alone: 15s - 14s + 3 = 14s - 14s - 13.
- Simplify to find the value of s: s = -16.
Therefore, the solution set is s = -16.